Test ideals in mixed characteristic: a unified theory up to perturbation
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arXiv
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| Autores principales: | , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913932821659648 |
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| author | Bhatt, Bhargav Ma, Linquan Patakfalvi, Zsolt Schwede, Karl Tucker, Kevin Waldron, Joe Witaszek, Jakub Datta, Rankeya |
| author_facet | Bhatt, Bhargav Ma, Linquan Patakfalvi, Zsolt Schwede, Karl Tucker, Kevin Waldron, Joe Witaszek, Jakub Datta, Rankeya |
| contents | Let $X$ be an integral scheme of finite type over a complete DVR of mixed characteristic. We provide a definition of a test ideal which agrees with the multiplier ideal after inverting $p$, is computed from a sufficiently large alteration, agrees with previous mixed characteristic BCM test ideals after completing at any point of residue characteristic $p$ (up to small perturbation), and which satisfies the full suite of expected properties of a multiplier or test ideal. This object is obtained via the $p$-adic Riemann-Hilbert functor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00615 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Test ideals in mixed characteristic: a unified theory up to perturbation Bhatt, Bhargav Ma, Linquan Patakfalvi, Zsolt Schwede, Karl Tucker, Kevin Waldron, Joe Witaszek, Jakub Datta, Rankeya Algebraic Geometry Commutative Algebra 14F18, 13A35 Let $X$ be an integral scheme of finite type over a complete DVR of mixed characteristic. We provide a definition of a test ideal which agrees with the multiplier ideal after inverting $p$, is computed from a sufficiently large alteration, agrees with previous mixed characteristic BCM test ideals after completing at any point of residue characteristic $p$ (up to small perturbation), and which satisfies the full suite of expected properties of a multiplier or test ideal. This object is obtained via the $p$-adic Riemann-Hilbert functor. |
| title | Test ideals in mixed characteristic: a unified theory up to perturbation |
| topic | Algebraic Geometry Commutative Algebra 14F18, 13A35 |
| url | https://arxiv.org/abs/2401.00615 |